I can only give you advice as a drinker, not as a brewer. I've never brewed an oyster stout, though I'd like to.
First of all, the phrase "oyster stout" in commercial beers can be misleading because not all all of them contain oysters (I think Marston's Oyster Stout, which is pretty easy to come by, is just water, yeast, hops, and malt. In any case it has no oyster component). So if you're interested in the style because of something you've had in a pub or from the store, then you might want to make sure that it actually had oysters. Even if a beer has (like in the case of Marston's) a sea-themed label, it doesn't necessarily have to have oysters in it.
There is a history of brewing with oysters in beer, though. I know that Dogfish Head has done it (but I don't know when and I think it was just for a festival - I just read about this in the founder's autobiography). I think the Porterhouse, originally from Dublin and now with a location in London (which I got to a year ago) actually uses oysters in the great beer they call Oyster Stout.
I can offer even less help on the actual process side, but I would be surprised if the actual meat were left in the boil for whole minutes. This is just a hunch given the fact that they're usually eaten raw and, if cooked, just cooked for seconds. The shells, I would guess, would be another story. I would think that whatever salts/minerals would come off the shell would be the main flavor imparted from those, and it might take more time to get a serious impression from them.